Linear solvers: Advanced options

This section targets advanced users and wants to help understanding what solver parameters do. Most advanced users who wants to select manually the solver to use and not only the type of solver must change their user mode: Flux Supervisor > Options > User mode > Advanced, then close and reopen Flux to apply that change. In the advanced mode, the solving options box displays significantly more options for linear solvers. Here is the list of linear solvers for instance:


Type	Solver Name	Parallel	Distributed
N/A	Automatic solver [default]	N/A	N/A
Iterative	ICCG[default]	No	No
	PETSc	Yes	Yes
	GMRes	No	No
	BICGStab	No	No
Direct	Mumps (Local) [default]	Yes	No
Direct	Mumps (Distributed)	Yes	Yes

For parallel and distributed solvers, you can set computing parameters globally in Flux Supervisor > Options > System > Parallel computing. These parameters are used to set some default options for Mumps and PETSc, see parallel computing for more details.

Below the details of each solver parameter is provided.

ICCG

ICCG is an iterative solver which uses the conjugate gradient for the solving and the incomplete Cholesky factorization of LDL^Tfor the preconditioning. In steady State AC, ICCG uses the conjugate bigradient for the solving and the incomplete factorization LDU for the preconditioning.

Options


Parameter	Description
Precision for the Conjugate Gradient	Relative precision to satisfy before stopping the iterative process. Default value: 1.0e-6
Maximum number of iterations for the Conjugate Gradient	Maximum number of iterations to compute before stopping the iterative process. Two options are available to set the number of iterations: A linear function which takes two integers as inputs (A and B) defined as: $N = A \times (n u m b e r o f d e g r e e s o f f r e e d o m) + B$ A fixed value N Default value: Linear function with A = 1 and B = 1, which is the number of equations of the problem.
Tolerance for the LDU preconditioning	Precision of the preconditioner. Default value: 1.0e-7
Print messages of the convergence evolution	Flag indicating to verbosity level of the iterative process. Set to “Yes” to prompt the evolution of the iteration process during the solving. Default value: “No”

PETSc

PETSc is a library of parallel and distribute iterative solvers. A pre-selection of pairs of solver/preconditioner was made depending on the dimension and type of problem. The process number is defined in Flux Supervisor, see parallel computing for details.

Options


Parameter	Description
Precision for the PETSc solver	Relative precision to satisfy before stopping the iterative process. Four options are available: Automatic, Low (1e-4), Medium (1e-8) and High (1e-12). Default value: Automatic
Maximum number of iterations	Maximum number of iterations to compute before stopping the iterative process. Default value:5,000

GMRes

GMRes is an iterative solver which uses the restart generalized minimum residual for the solving and the incomplete factorization with ILUT for the preconditioning.

Options


Parameter	Description
Precision for GMRes	Relative precision to satisfy before stopping the iterative process. Default value: 1.0e-6
Maximum number of iterations for the GMRes	Maximum number of iterations to compute before stopping the iterative process. Two options are available to set the number of iterations: A linear function which takes two integers as inputs (A and B) defined as: $N = A \times (n u m b e r o f d e g r e e s o f f r e e d o m) + B$ A fixed value N Default value: Linear function with A = 1 and B = 1, which is the number of equations of the problem.
Tolerance for the ILUT preconditioning	Precision of the preconditioner. Default value: 1.0e-6
Coefficient for the level of fill for the ILUT preconditioning	Filling factor of the ILUT preconditioner. Default value: 6.0
Dimension of the Krylov space	Number of vectors to store in order to build Krylov space. Default value: 120
Print messages of the convergence evolution	Flag indicating to verbosity level of the iterative process. Set to “Yes” to prompt the evolution of the iteration process during the solving. Default value: “No”

BiCGStab

BiCGStab is an iterative solver which uses the stabilized conjugate bi-gradient for the solving and the incomplete Choleski factorization of LDL^Tfor the preconditioning. In steady State AC, BiCGStab uses incomplete factorization LDU for the preconditioning

Options


Parameter	Description
Precision for the BiCGStab	Relative precision to satisfy before stopping the iterative process. Default value: 1.0e-6
Maximum number of iterations for BiCGStab	Maximum number of iterations to compute before stopping the iterative process. Two options are available to set the number of iterations: A linear function which takes two integers as inputs (A and B) defined as: $N = A \times (n u m b e r o f d e g r e e s o f f r e e d o m) + B$ A fixed value N Default value: Linear function with A = 1 and B = 1, which is the number of equations of the problem.
Tolerance for the LDU preconditioning	Precision of the preconditioner. Default value: 1.0e-7
Print messages of the convergence evolution	Flag indicating to verbosity level of the iterative process. Set to “Yes” to prompt the evolution of the iteration process during the solving. Default value: “No”

Mumps

Mumps is a direct solver, based on a multi frontal approach.

Mumps (Local) is a mono-process, but multithread solver. There is only one process while number of threads is fixed by cores number choose by the user from the Flux Supervisor.

Mumps (Distributed) is a multi-process and multithread solver. Process and thread numbers are defined in Flux Supervisor, see parallel computing for details.

Options


Parameter	Description
Verbosity level	Set the level of verbosity during the solving process. Four levels are available to decide what information will be prompted: 1- Only errors messages 2- Errors, warnings and main statistics 3- Errors, warnings and terse diagnostics 4- Errors, warnings and information on input and output parameters Default value: “1- Only errors messages”
Using disk memory	Set the options regarding disk usage. Four options are available: No, do not use the disk memory Automatic – Switch over to Out-of-core depending on the matrix size Yes – Default temporary directory Yes – Choice of the temporary directory Default value: “No”
Reordering method	Set the reordering method to use. Five methods can be used: METIS AMD – Approximate Minimum Degree QAMD – AMD with quasi-dense rows detection PORD AMF Default value: “Automatic – Choice in Mumps”
Memory limitation (RAM)	Set the memory limitation. It allows the user to limit the memory Mumps can use (in MB). Default value: Unlimited
MPI Options	Only for MUMPS (Distributed). Set to define MPI Options. To enable MPI computations, the MPI number can be specified with the Thread number. Default value: “No"